Butterfly effect in a circle

Balls falling under gravity in a circle is another example of a chaotic system, sometimes referred to as the butterfly effect.

@gpcbass reproduced the absolutely brilliant composition "Jesus bleibet meine Freude", originally made by J S Bach almost 300 years ago. A full version can be found here    • Fender Jazz Bass 1962 and Fender Prec...   and here    • Jesus, bleibet meine Freude (J S Bach)  .

Further details:
1. One ball in a circle having radius R
2. Two balls separated by 0.01*R
3. 100 balls, each pair being separated by 1e-6*R.

Done in Python and FFmpeg. SymPy was used to solve some equations.

Visuals inspired by @Numberphile,    • Chaotic Balls (and other animations) ...